Papers by Umberto Villa
We propose two multilevel spectral techniques for constructing coarse discretization 4 spaces for... more We propose two multilevel spectral techniques for constructing coarse discretization 4 spaces for saddle-point problems corresponding to PDEs involving divergence constraint, with fo-5 cus on the mixed finite element discretization of scalar self-adjoint second order elliptic equations 6 on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe) which 7 employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid 8 elements. The coarse basis associated with each agglomerated coarse element is constructed by solv-9 ing local eigenvalue problems and local mixed finite element problems. This construction leads to 10 stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. 11 Also, approximation properties of these upscaling spaces improve by adding more local eigenfunc-12 tions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, 13 as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) 14 deteriorates as we introduce additional functions in the coarse space. We also provide an efficient 15 solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a 16 s.p.d. reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use 17 our previously developed spectral AMGe solver. Numerical experiments, in both 2D and 3D, are 18 provided to illustrate the efficiency of the proposed upscaling technique.
High Performance Computing (HPC) is a mainstream mode of exploration and analysis in different fi... more High Performance Computing (HPC) is a mainstream mode of exploration and analysis in different fields, not only technical but also social and life sciences. A well established HPC domain is medicine, and cardiovascular sciences in particular. The adoption of CFD as a tool for diagnosis, prognosis, and treatment planning in the clinical routine is however still an open challenge. This computational tool, required by Computer Aided Clinical Trials and Surgical Planning, calls for significant computational resources to face both large volume of patients and diverse timelines ranging from election to emergency scenarios. Traditional local clusters may be not adequate to deliver the computational needs. Alternative solutions like grids and on-demand cloud resources need to be seriously considered. This paper proposes methodologies and protocols to identify the optimal choice of computing platforms for hemody-namics computations that will be increasingly needed in the future and the optimal scheduling of the tasks across the selected resources. We focus on hemodynamics in patient-specific settings and present extensive results on different platforms. We propose a way to measure and estimate performance and running time under realistic
This work considers the combined space-time discretization of time-dependent partial differential... more This work considers the combined space-time discretization of time-dependent partial differential equations by using first order least square methods. We also impose an explicit constraint representing space-time mass conservation. To alleviate the restrictive memory demand of the method, we use dimension reduction via accurate element agglomeration AMG coarsen-ing, referred to as AMGe upscaling. Numerical experiments demonstrating the accuracy of the studied AMGe upscaling method are provided.
We study the application of a finite element numerical upscaling technique to the incompressible ... more We study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element-agglomeration based Algebraic Multigrid (AMGe) technique with improved approximation properties [37] is used, for the first time, to generate upscaled and accurate coarse systems for the reservoir simulation equations. The upscaling technique is applied to both the mixed system for velocity and pressure and to the hyperbolic transport equations providing fully upscaled systems. By introducing additional degrees of freedom associated with non-planar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart-Thomas and piecewise discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured and unstructured meshes. Multiscale Mixed Finite Elements exhibit accuracy for general unstructured meshes but do not in general lead to nested hierarchy of spaces. Multiscale multilevel mimetic finite differences generate nested spaces but lack the adaptivity of the flux representation on coarser levels that the proposed AMGe approach offers. Thus, the proposed approach can be seen as a rigorous bridge that merges the best properties of these two existing methods. The accuracy and stability of the studied multilevel AMGe upscaling technique is demonstrated on two challenging test cases.
The international journal of behavioral nutrition and physical activity, Jan 20, 2015
The objectives of this study were to describe the accelerometer based total and bout-specific PA ... more The objectives of this study were to describe the accelerometer based total and bout-specific PA levels for a representative sample of adults from Cuernavaca, Mexico, and to examine the relationships with sociodemographic characteristics and BMI status. Cross sectional study of adults from Cuernavaca, Mexico (2011, n = 677). Participants wore Actigraph GT3X accelerometers for seven days and sociodemographic data was collected through a survey. Weight and height were objectively measured. Total minutes/week of moderate-to-vigorous PA (MVPA) and of MVPA occurring within bouts of at least ten minutes were obtained. Intensity-specific (moderate and vigorous) total PA and bouted-PA was also obtained. The relation of each PA variable with sex, age, socioeconomic status, education, marital status and BMI status was assessed using unadjusted and adjusted linear models. The mean total MVPA among adults from Cuernavaca was 221.3 ± 10.0 (median = 178.3 min/week). Average MVPA within bouts was ...
2014 IEEE International Conference on Cloud Engineering, 2014
We discuss in this paper the validation of an open source framework for the solution of problems ... more We discuss in this paper the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for fluid flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms to solve both fluid and fluid-structure interaction problems. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. The numerical fluid-structure interaction benchmark deals with the propagation of a pressure wave in a fluidfilled elastic tube. The computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. A detailed account of the methods used for both benchmarks is provided.
This paper demonstrates an application of element-based Algebraic Multigrid (AMGe) technique deve... more This paper demonstrates an application of element-based Algebraic Multigrid (AMGe) technique developed at LLNL (19) to the numerical upscaling and preconditioning of subsurface porous media flow problems. The upscaling results presented here are further extension of our recent work in 3. The AMGe approach is well suited for the solution of large problems coming from finite element discretizations of systems of partial differential equations. The AMGe technique from 10,9 allows for the construction of operator-dependent coarse (upscaled) models and guarantees approximation properties of the coarse velocity spaces by introducing additional degrees of freedom associated with non-planar interfaces between agglomerates. This leads to coarse spaces which maintain the specific desirable properties of the original pair of Raviart-Thomas and piecewise discontinuous polynomial spaces. These coarse spaces can be used both as an upscaling tool and as a robust and scalable solver. The methods employed in the present paper have provable O(N) scaling and are particularly well suited for modern multicore architectures, because the construction of the coarse spaces by solving many small local problems offers a high level of concurrency in the computations. Numerical experiments demonstrate the accuracy of using AMGe as an upscaling tool and comparisons are made to more traditional flow-based upscaling techniques. The efficient solution of both the original and upscaled problem is also addressed, and a specialized AMGe preconditioner for saddle point problems is compared to state-of-the-art algebraic multigrid block preconditioners. In particular, we show that for the algebraically upscaled systems, our AMGe preconditioner outperforms traditional solvers. Lastly, parallel strong scaling of a distributed memory implementation of the reservoir simulator is demonstrated.
The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equat... more The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem. Introducing the flow's vorticity as additional unknown, this formulation allows for a uniformly stable and conforming discretization by standard finite elements (Nédélec, Raviart-Thomas, piecewise discontinuous). The theoretical results are illustrated with numerical experiments. Based on our stability analysis of the problem in the H(curl; Ω)−H(div; Ω)− L 2 (Ω) norms, we derive, in a follow-up paper ([34]), a scalable block diagonal preconditioner which takes advantage of the auxiliary space AMG solvers for H(curl) and H(div) problems available in the preconditioning library hypre ([19]) developed at LLNL.
The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equat... more The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow's vorticity as an additional unknown. This formulation allows for a uniformly stable and conforming discretization by standard finite element (Nédélec, Raviart-Thomas, discontinuous piecewise polynomials). Based on the stability analysis of the problem in the H(curl) − H(div) − L 2 norms ([24]), we study a scalable block diagonal preconditioner which is provably optimal in the constant coefficient case. Such preconditioner takes advantage of the parallel auxiliary space AMG solvers for H(curl) and H(div) problems available in hypre ([11]). The theoretical results are illustrated by numerical experiments.
In the first part of this work we have introduced a time adaptive solver for the incompressible N... more In the first part of this work we have introduced a time adaptive solver for the incompressible Navier-Stokes equations based on the pressure correction splitting advocated by Saleri and Veneziani (2005). This scheme computes the pressure as a sequence of intermediate guesses featuring an increasing order of accuracy. The comparison of two different guesses provides a natural a posteriori error estimator (with no additional cost) for the automatic selection of the time step. Basic formulation of the methods and possible variants have been addressed in Part 1. In this Part 2 we consider in detail the implementation of the method. After discussing mass lumping techniques for high order finite elements, we describe data structures and solvers for the computation of the pressure. Several numerical results in 3D are presented showing the effectiveness of the approach. We present a test case of blood flow simulation in a human aorta retrieved from medical images. Computational hemodynamics features problems with a sequence of fast and slow transients and it is therefore supposed to largely benefit from a time-adaptive solver. This work is dedicated to the memory of F. Saleri.
We address a time-adaptive solver specifically devised for the incompressible Navier-Stokes equat... more We address a time-adaptive solver specifically devised for the incompressible Navier-Stokes equations. One of the challenging issues in setting up a timeadaptive solver is the identification of a reliable a-posteriori error estimator. Typical strategies are based on the combination of the solutions computed either with two different time steps or two schemes with different accuracy. In this paper we move from the pressure correction algebraic factorizations formerly proposed by Saleri, Veneziani (2005). These schemes feature an intrinsic hierarchical nature, such that an accurate solution for the pressure is obtained by computing an intermediate low-order guess. The difference between the two estimates provide a natural a-posteriori estimator. In this first part we address the properties of this approach, and its possible variants, including the pressure incremental formulation. Numerical results refer to 2D test cases. The second part will cover implementation details and results in 3D. This work is dedicated to the memory of F. Saleri.
We discuss in this paper the validation of an open source framework for the solution of problems ... more We discuss in this paper the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for steady flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms to solve both fluid and fluid-structure interaction problems. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. The numerical fluid-structure interaction benchmark deals with the propagation of a pressure wave in a fluid-filled elastic tube. The computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. A detailed account of the methods used for both benchmarks is provided.
In this study we characterize the rheology of fluidized granular matter subject to secondary forc... more In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation, and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterize by the GDR-Midi model if the system is forced with slow oscillations. The model breaks down when the forcing timescale becomes comparable to characteristic time for energy dissipation in the flow.
Heterogeneity in secondary characteristics of different HPC target platforms is the focus of this... more Heterogeneity in secondary characteristics of different HPC target platforms is the focus of this paper. Clusters, grids, and (IaaS) clouds may appear straightforward to configure to be interchangeable -but our experiences with mainstream parallel codes for CFD demonstrate that secondary attributes -support software, interconnect type, availability, access, and cost -expose heterogeneous aspects that impact overall effectiveness of application execution. The emergence of clouds as alternatives to grids and local resources for parallel HPC codes portends "computing as a utility" in science and engineering domains. Our experiences provide preliminary insights into characterizing these different types of platforms to which users typically have access -and show where the tradeoffs can be, in terms of deployment effort, actual and nominal costs, application performance, and availability (both in terms of resource size and time to gain access). For our test application, we report that each of the platforms to which we had access had its particular benefits and drawbacks in terms of the above attributes. More generally, our experiences may provide an example preview into what developers and users can expect when selecting a "utility provider" and specific instance thereof for a particular run of their application.
Heterogeneity is often manifested in different forms even in environments that seem to be similar... more Heterogeneity is often manifested in different forms even in environments that seem to be similar. In particular, clusters, grids, and infrastructure as a service (IaaS) clouds may appear straightforward to configure to be interchangeable. However, our experiences with mainstream parallel codes for solving complex computational fluid dynamics (CFD) problems demonstrate that secondary attributes -support software, interconnect type, availability, access, and cost -expose heterogeneous aspects that impact overall effectiveness of application execution as well as overall productivity. Our experiences provide preliminary insights into characterizing three different types of platforms to which users typically have access -local clusters, grids, and clouds -and show where the tradeoffs can be, in terms of deployment effort, actual and nominal costs, application performance, and availability (both in terms of resource size and time to gain access). The considered benchmark is the numerical solution of partial differential equations for a blood flow problem. For this application, we compare five platforms with respect to two metrics: time to completion and cost per simulation. We further introduce a third metric, the utility function of the simulation, and discuss different user profiles leading to different rankings of the tested platforms. Additionally, we propose a systematic approach to overcome heterogeneity introduced by software dependencies required for application execution. Our results suggest that IaaS clouds are a viable approach for intensive CFD simulations.
Thesis Chapters by Umberto Villa
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Papers by Umberto Villa
Thesis Chapters by Umberto Villa